﻿106 
  Prof. 
  Sudhansukumar 
  Banerji 
  on 
  Aerial 
  

  

  The 
  values 
  in 
  different 
  directions 
  have 
  been 
  calculated 
  

   from 
  these 
  expressions 
  and 
  are 
  shown 
  in 
  the 
  following 
  

   table 
  : 
  — 
  

  

  

  

  Table 
  II. 
  

  

  

  Angles 
  

   (in 
  degrees). 
  

  

  F 
  X 
  const. 
  

  

  G 
  X 
  const. 
  

  

  (F 
  2 
  +G 
  2 
  ) 
  X 
  const. 
  

  

  

  

  +900000 
  

  

  + 
  38000 
  

  

  811444 
  

  

  10 
  

  

  +890608 
  

  

  + 
  28804 
  

  

  794265 
  

  

  20 
  

  

  + 
  849305 
  

  

  - 
  2390 
  

  

  720805 
  

  

  30 
  

  

  +752167 
  

  

  - 
  45754 
  

  

  567620 
  

  

  40 
  

  

  +572469 
  

  

  - 
  90446 
  

  

  335284 
  

  

  50 
  

  

  +309902 
  

  

  -123998 
  

  

  111476 
  

  

  60 
  

  

  - 
  5783 
  

  

  - 
  135346 
  

  

  18261 
  

  

  70 
  

  

  -313014 
  

  

  -118446 
  

  

  111893 
  

  

  80 
  

  

  -542728 
  

  

  - 
  73554 
  

  

  300178 
  

  

  90 
  

  

  -635375 
  

  

  - 
  9000 
  

  

  403306 
  

  

  100 
  

  

  -571364 
  

  

  + 
  60786 
  

  

  329762 
  

  

  110 
  

  

  -371618 
  

  

  + 
  118638 
  

  

  154545 
  

  

  120 
  

  

  - 
  96799 
  

  

  + 
  149218 
  

  

  31610 
  

  

  130 
  

  

  +184472 
  

  

  + 
  144494 
  

  

  54592 
  

  

  140 
  

  

  +412409 
  

  

  + 
  105758 
  

  

  180980 
  

  

  150 
  

  

  +559907 
  

  

  + 
  44650 
  

  

  315625 
  

  

  160 
  

  

  +630625 
  

  

  - 
  21410 
  

  

  398602 
  

  

  170 
  

  

  +654606 
  

  

  - 
  69748 
  

  

  433925 
  

  

  180 
  

  

  +658000 
  

  

  - 
  88000 
  

  

  440708 
  

  

  The 
  values 
  of 
  F 
  2 
  + 
  G 
  2 
  shown 
  in 
  Tables 
  I. 
  and 
  II., 
  have 
  

   been 
  plotted 
  in 
  polar 
  coordinates 
  in 
  figs. 
  3 
  and 
  4 
  (PI. 
  IV.). 
  

   It 
  is 
  seen 
  that 
  in 
  both 
  cases 
  the 
  intensity 
  in 
  the 
  direction 
  of 
  

   the 
  larger 
  ball 
  is 
  greater 
  than 
  in 
  the 
  direction 
  of 
  the 
  smaller 
  

   ball. 
  The 
  asymmetry 
  is 
  more 
  marked 
  when 
  k(a-\-b) 
  has 
  

   the 
  larger 
  value. 
  

  

  The 
  intensity 
  of 
  the 
  sound 
  in 
  different 
  directions 
  due 
  to 
  

   the 
  impact 
  of 
  two 
  spheres 
  of 
  wood 
  of 
  diameters 
  3 
  inches 
  and 
  

   1^ 
  inches 
  respectively 
  has 
  been 
  measured 
  with 
  the 
  ballistic 
  

   phonometer 
  and 
  ig 
  shown 
  in 
  fig. 
  5. 
  It 
  is 
  seen 
  that 
  this 
  

   curve 
  is 
  intermediate 
  in 
  form 
  between 
  those 
  shown 
  in 
  fig. 
  3 
  

   and 
  fig. 
  4, 
  exactly 
  as 
  anticipated. 
  The 
  agreement 
  between 
  

   theory 
  and 
  experiment 
  is 
  thus 
  very 
  striking 
  in 
  this 
  case. 
  

  

  